Control systems and control theory are well-developed fields of research and development that have had a profound impact on the design and development of a large number of systems and technologies, from airplanes, spacecraft, and other vehicle and 20 transportation systems to computer systems, industrial manufacturing and operations facilities, machine tools, process machinery, and consumer devices. Control theory encompasses a large body of practical, system-control-design principles, but is also an important branch of theoretical and applied mathematics. Various different types of controllers are commonly employed in many different application domains, from simple closed-loop feedback controllers to complex, adaptive, state-space and differential-equations-based processor-controlled control system.
Many controllers are designed to output control signals to various dynamical components of a system based on a control model and sensor feedback from the system. Many systems are designed to exhibit a predetermined behavior or mode of operation, and the control components of the system are therefore designed, by traditional design and optimization techniques, to ensure that the predetermined system behavior transpires under normal operational conditions. A more difficult control problem involves design and implementation of controllers that can produce desired system operational behaviors that are specified following controller design and implementation. Theoreticians, researchers, and developers of many different types of controllers and automated systems continue to seek approaches to controller design to produce controllers with the flexibility and intelligence to control systems to produce a wide variety of different operational behaviors, including operational behaviors specified after controller design and manufacture.